Mathieu Bédard and Vincent Geloso have a paper out on SSRN here, "Free Banking and Economic Growth in Lower Canada, 1817-1851":

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482313#.U_HwDx1w4a0.facebook

Says the abstract:

Generally, the historical literature presents the period from 1817 to 1851 in Lower Canada (modern day Québec) as one of negative economic growth. This period also coincides with the rise of free banking in the colony. In this paper we propose to study the effects of free banking on economic growth using theoretical and empirical validations to study the issue of whether or not economic growth was negative. First of all, using monetary identities, we propose that given the increase in the stock of money and the reduction in the general price level, there must have been a positive rate of economic growth during the period. We also provide complementary evidence drawn from wages that living standards were increasing. It was hence impossible for growth to have been negative. Secondly, we propose that the rise of privately issued paper money under free banking in the colony had the effect of mitigating the problem of the abundance of poor quality coins in circulation which resulted from legal tender legislation. It also had the effect of facilitating credit networks and exchange. We link this conclusion to the emergence of free banking which must have been an important contributing factor. Although we cannot perfectly quantity the effect of free banking on economic growth in Lower Canada, we can be certain that its effect on growth was clearly positive.